ON9CD (Vandonselaar 2002) gives an expose on baluns for Hams.
Above is the first diagram he gives in support of his explanation.
He goes on to give the relation:
Zin = u / i which is equal to Rb
The equation is mathematical proof that it is a 1:1 balun… or is it?
Note that the current into the coax on the left is i and the current out of the coax on the right is also i.
In the real world, this CANNOT happen, not even for a transmission line with no standing waves… there is some amplitude change and some phase change.
Likewise, the voltages at each end of the lines are not exactly equal as stated.
Whilst the amplitude change might typically be small in this application, the phase change is significant at the upper limit of the devices usable frequency range.
For example, you might well wind a device of this type with a 1m length of RG316 on each core. The current out of a 1m section of RG316 with a load of 50+j0Ω is 0.9917 of the amplitude of the input, and delayed by 52.5°, and although the coax is nominally 50+j0Ω, practical coax lines have some small reactive component, in this case Zo=50.01-j0.88Ω at 30MHz, and there is a small standing wave, and impedance transformation, Zin=50.84-j1.09Ω.
This might seem inconsequential, but what if the load was 50+j50Ω, Zin=76.93-j56.11Ω. It is hardly a 1:1 transformer in the general sense, though the equation quoted above states just that.
The whole description of these type of devices is afflicted with an assumption that the transmission line sections have no loss and no phase change, and that is not true for practical devices.
It is an explanation that will appeal to simple minds who haven’t gotten beyond being totally satisfied by simple explanations, explanations that don’t apply strictly to real world things and in this case cannot explain one of the main reasons why these things have an upper limit to their usable frequency range.
- Vandonselaar, B. 2002. Ferrites in HF applications. http://sharon.esrac.ele.tue.nl/~on9cvd/E-Transmissielijn%20trafo,%20inleiding%20en%20achtergrond.htm (accessed 29/04/14).